Finite Group DatabasebetaFinite Group Databasebeta| order | 7499 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C23×C163 (order 7498) · Inn(G) = C1 · Out(G) = C2×C23×C163 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C7499 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
2 conjugacy classes of subgroups.
7499 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic7499, C2×D7499 |
| maximal subgroup of | D7499, C2×C7499, C3×C7499, … |
| maximal normal subgroup of | D7499, C2×C7499, C3×C7499, … |
| maximal quotient of | C2×C7499, C3×C7499, C5×C7499 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7499, 1);